"The flu spreads easily among children,” professor Jan Liliemark from Sweden's Medical Products Agency (Läkemedelsverket) said in a statement.
"Kids under the age of four risk being hit worst by the infection."
Pandramrix, the vaccine used in Sweden, is medically approved for children from the age of six months.
But Swedish authorities have chosen not to recommend routine vaccinations to children under the age of three because information about side effects on small children is scarce.
The decision is based on various grounds, partly in relation to a recent Spanish study where 51 small children where vaccinated.
Other grounds for the recommendation include feedback within Sweden on the vaccine's side effects and the fact that 5,000 young children in high-risk groups have already been vaccinated.
The biggest increase has been noting among children under the age of four.
The latest prognosis from the European Centre for Disease Prevention and Control suggest that around that one million Swedes will contract the A/H1N1 virus before the pandemic is over.
The agency states that countries should prepare for at least 20 percent of the population to become infected without widespread vaccination. But an early vaccination programme has halved that figure for Sweden.
”That figure sounds reasonable”, said Annika Linde from Smittskyddsinstitutet.
”But had it not been for the vaccination campaign the figure would have been a lot higher.”
Three million Sweden have already had the jab and it is estimated that around half the population will be vaccinated within a month.